Taiwanese Journal of Mathematics

SOME FAMILIES OF INFINITE SERIES SUMMABLE BY MEANS OF FRACTIONAL CALCULUS

K. Nishimoto, Shih-Tong Tu, and I-Chun Chen

Full-text: Open access

Abstract

In a Five-volume work published recently, K. Nishimoto [1] has presented a systematic account of the theory and applications of fractional calculus in a number of areas (such as ordinary and partial differential equations, special functions, and summation of series). In 2001, K. Nishimoto, D.-K. Chyan, S.-D. Lin and S.-T. Tu [11] derived the following interesting families of infinite series via fractional calculus, $$ \displaystyle\sum_{k=2}^{\infty}\ \frac{(-c)^k}{k(k-1)}\frac{(kz-c)}{(z-c)^{k-1}}=c^2\ \biggr(\biggr|\displaystyle\frac{-c}{z-c}\biggr|\lt 1\biggr).$$ The object of the present paper is to extend the above families of infinite series to more general closed form relations. Various numerical results are also provided.

Article information

Source
Taiwanese J. Math., Volume 6, Number 4 (2002), 465-474.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407471

Digital Object Identifier
doi:10.11650/twjm/1500407471

Mathematical Reviews number (MathSciNet)
MR1937472

Zentralblatt MATH identifier
1027.26006

Subjects
Primary: 26A33: Fractional derivatives and integrals 33C20: Generalized hypergeometric series, $_pF_q$
Secondary: 33B15: Gamma, beta and polygamma functions

Keywords
fractional calculus infinite series infinite sums

Citation

Nishimoto, K.; Tu, Shih-Tong; Chen, I-Chun. SOME FAMILIES OF INFINITE SERIES SUMMABLE BY MEANS OF FRACTIONAL CALCULUS. Taiwanese J. Math. 6 (2002), no. 4, 465--474. doi:10.11650/twjm/1500407471. https://projecteuclid.org/euclid.twjm/1500407471


Export citation